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The Uncertainty Principle  A signal cannot be localized arbitrarily well both in time/position and in frequency/momentum.  There exists a lower bound to the Heisenberg’s product:Heisenberg’s product  t  f  1/(4  ) Improving on this bound would result in sonars with better temporal resolution at a given frequency range  f = 10kHz,  t = 50 sec ~ 10cm

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Fundamental Research Questions Data Representation Is the more detailed Time/Frequency analysis robust Due to the very short time of the pulse, can a detailed representation be estimated Data Analysis Is the signal generation of Dolphins robust up to such details Can we gain more information from this detailed representation

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Echo localization Echo can be measured at this frequency Echo can be measured at this frequency Echo can also be measured here Time in microSec

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Bat sonar echo localization (Simulated) Time in microSec

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Click Classification using Time Frequency Analysis Thanks to Maryam Saleh and Juda Jacobson Told you… and don’t make a mistake next time

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Goals Asses the relevance of Time/Frequency analysis to dolphin clicks Asses the robustness of the of dolphin clicks to the details of the time frequency analysis Can we gain more information from this detailed representation Study the click sequence structure Study variability due to task and other environmental conditions

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Time/Frequency analysis Allows a detailed analysis of the click where the time location of each frequency component is displayed. The clicks above show some tilt in time when going From low to high frequencies. X axis is time in microseconds, Y axis freq. in Mhz.

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Time series plot of 98 consecutive clicks (File R0606C09)

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Fourier plots of the clicks (File R0606C09)

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Time-frequency representations (File R0606C09)

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15 Fourier PC’s generated from 1360 clicks (Rake Saline)

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15 Time/Freq PC’s generated from 1360 clicks (Rake Saline)

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Dendrogram of the projections of R0606C09 onto the PCs (time-frequency)

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Preliminary conclusions The detailed time/frequency analysis appears to be relevant to dolphin signals The dolphin is generating a collection of signals that can not be explained by a (single) signal + noise model First clicks are very different than last ones (Need to match with Ted’s results) There is interesting cluster structure of the clicks in high dimension

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Future directions The detailed time/frequency analysis appears to be relevant to dolphin signals The dolphin is generating a collection of signals that can not be explained by a (single) signal + noise model First clicks are very different than last ones (Need to match with Ted’s results) There is interesting cluster structure of the clicks in high dimension